examview - ch 2 test review · ch 2 test review making conjectures: conjectures about angles formed...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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CH 2 Test Review

Making Conjectures: Conjectures about Angles Formed by Parallel Lines Cut by a Transversal

Use the given information to determine the measures of all unknown angles in each figure. Give a

supporting reason. Use complete sentences to explain how you found your answers

m∠4 = 65°

Angle Measure Reason

m∠1 =

m∠2 =

m∠3 =

m∠4 = 65°

m∠5 =

m∠6 =

m∠7 =

m∠8 =

1. m∠6 = 89°

Angle Measure Reason

=

=

=

=

=

m∠6 = 89°

=

Name: ________________________ ID: A

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2. m∠4 = 95°

Angle measure Reason:

m∠1 =

m∠2 =

m∠3 =

m∠4 = 95°

m∠5 =

m∠6 =

m∠7 =

m∠8 =

Name: ________________________ ID: A

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Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior Angle

Theorem, and Same-Side Exterior Angle Theorem

Prove each statement using the indicated type of proof.

Use a paragraph proof to prove the Alternate

Interior Angles Theorem. In your proof, use

the following information and refer to the

diagram.

Given: a Ä b, c is a transversal

Prove: ∠2 ≅ ∠8

3.

Use a two-column proof to prove the Alternate

Exterior Angles Theorem. In your proof, use the

following information and refer to the diagram.

Given: r Ä s, t is a transversal

Prove: ∠4 ≅ ∠5

Statements Reasons

Name: ________________________ ID: A

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A Reversed Condition: Parallel Line Converse Theorems

Write the converse of each statement.

EXAMPLE:

If a triangle has three congruent sides, then the triangle is an equilateral triangle.

Converse: If a triangle is an equilateral triangle, then the triangle has three congruent sides.

.

4. If a figure is a rectangle, then it has four sides.

.

5. If two angles in a triangle are congruent, then the triangle is isosceles.

.

Name: ________________________ ID: A

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If two lines, cut by a transversal, form same-side

exterior angles that are supplementary, then the lines

are parallel.

Given: ____________________________________

Prove:____________________________________

.

6.

If two lines, cut by a transversal, form alternate interior

angles that are congruent, then the lines are parallel.

Given: ____________________________________

Prove:____________________________________

.

Name: ________________________ ID: A

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Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior Angle

Theorem, and Same-Side Exterior Angle Theorem

Use the diagram to write the “given” and “prove” statements for each theorem.

EXAMPLE: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the

transversal are supplementary.

Given: r Ä c, n is a transversal

Prove: ∠1 and ∠7 are supplementary or ∠2 and

∠8 are supplementary

7.

If two parallel lines are cut by a transversal, then the

alternate interior angles are congruent.

Given: ____________________________________

Prove:____________________________________

Name: ________________________ ID: A

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Prove each statement using the indicated type of proof.

Use a paragraph proof to prove the Alternate Exterior Angles Converse Theorem. In your proof, use the


Given: ∠4 ≅ ∠5, j is a transversal

Prove: p Ä x

8. Use a two column proof to prove the Alternate Interior Angles Converse Theorem. In your proof, use the


Given: ∠2 ≅ ∠7, k is a transversal

Prove: m Ä n

Statements Reasons

Name: ________________________ ID: A

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9. Use a flow chart to prove the Same Side Interior Angles Converse Theorem. In your proof, use the following

information and refer to the diagram.

Given: ∠6 and ∠7 are supplementary, e is a transversal

Prove: f Ä g

Define the reasons on the Word Bank below::

∠5 and ∠6 are a linear pair

∠6 and ∠7 are supplementary

∠5 and ∠6 are supplementary

g II f

∠5 ≅ ∠7

Corresponding Angle Postulate-

____________________________________

______________________________

Definition of linear pair

____________________________________

______________________________

Given

____________________________________

______________________________

Linear Pair Postulate

____________________________________

______________________________

Substitution Property

____________________________________

______________________________

Name: ________________________ ID: A

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Many Sides: Naming Geometric Figures

Classify each polygon shown.

Example

triangle

10. ____________________

11. ____________________

12. ____________________

13. ____________________

14. ____________________

Name: ________________________ ID: A

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15. ____________________

16. ____________________

Quads and Tris: Classifying Triangles and Quadrilaterals

Draw an example of each term.

17. equiangular triangle

.

18. scalene triangle

.

19. right triangle

.

Name: ________________________ ID: A

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20. In the figure, line c is parallel to line d and m∠3 = 26°. Determine the measure of ∠6 using the

Corresponding Angle Postulate and any other theorems, postulates, or properties.

Name: ________________________ ID: A

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21.

Use the figure to prove the Alternate Interior Angle

Converse Theorem.

Given: ∠4 ≅ ∠6

Prove: ™ Ä m

Define each reason on the Word bank below:

Corresponding Angle Converse Postulate

___________________________________________________________________________

_______________________________________________________________

Given

___________________________________________________________________________

_______________________________________________________________

Transitive Property

___________________________________________________________________________

_______________________________________________________________

Vertical Angle Theorem

___________________________________________________________________________

_______________________________________________________________

Name: ________________________ ID: A

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22. The lines shown in the figure are parallel, and m∠1 = 102°. Determine the missing angle measures without

using a protractor. Explain how you calculated your answers.

Statements Reasons

m∠ 1 = 102°

m∠ 2 =

m∠ 3 =

m∠ 4 =

m∠ 5 =

m∠ 6 =

m∠ 7 =

m∠ 8 =

.

23. Consider the statement “If a quadrilateral is a square, then the quadrilateral is a rectangle.”

a. Identify the hypothesis of the statement.

b. Identify the conclusion of the statement.

c. Write the converse of the statement.

Name: ________________________ ID: A

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Making Conjectures: Conjectures about Angles Formed by Parallel Lines Cut by a Transversal

24. Construct line p parallel to line b such that line m is a transversal.

.

Name: ________________________ ID: A

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Solve for x in each figure. Show all your work. Give the measurement of all angles; Explain your

reasoning.

.

25.

Measure Reason

m∠1 =

m∠2 =

m∠3 =

m∠4 =

m∠5 =

m∠6 =

m∠7 =

m∠8 =

26.

Measure Reason

m∠1 =

m∠2 =

m∠3 =

m∠4 =

m∠5 =

m∠6 =

m∠7 =

m∠8 =

Name: ________________________ ID: A

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.

27. Use the figure to determine the measure of each indicated angle. SHOW ALL YOUR WORK.

a. m∠EGA= _____

b. m∠CHF= _____

c. m∠FHD= _____

d. m∠EGB= _____

Name: ________________________ ID: A

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28. Use the figure to write the postulate, theorem, or converse theorem that justifies each statement.

a. m∠1 = m∠8, so a Ä b - __________________________________________________

b. m∠4 + m∠6 = 180°, so a Ä b- _____________________________________________

c. a Ä b, so m∠3 = m∠7- __________________________________________________

d. m∠2 + m∠8 = 180°, so a Ä b- _____________________________________________

e. m∠4 = m∠5, so a Ä b- __________________________________________________

f. a Ä b , so m∠3 + m∠5 = 180°- _____________________________________________

Name: ________________________ ID: A

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29. Use the given information to determine the pair of lines that are parallel. Write the postulate or theorem that

justifies your answer.

a. m∠4 = m∠5- _________________________________________________________

b. m∠2 + m∠12 = 180°- __________________________________________________

c. m∠7 = m∠11- _______________________________________________________

d. m∠8 + m∠10 = 180°- __________________________________________________

e. m∠1 + m∠7 = 180°- ___________________________________________________

f. m∠2 = m∠11- ________________________________________________________

ID: A

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CH 2 Test Review

Answer Section

1. ANS: m∠1 = 89°, m∠2 = 91°, m∠3 = 89°, m∠4 = 91°, m∠5 = 91°, m∠7 = 91°, m∠8 = 89°

PTS: 1 REF: Ch2.2 TOP: Skills Practice

2. ANS: m∠1 = 85°, m∠2 = 95°, m∠3 = 85°, m∠5 = 85°, m∠6 = 95°, m∠7 = 85°, m∠8 = 95°


3. ANS:

Statements Reasons

1. r Ä s, t is a transversal

2. ∠4 ≅ ∠2

3. ∠2 ≅ ∠5

4. ∠4 ≅ ∠5

1. Given

2. Corresponding Angles Postulate

3. Vertical Angles Congruence Theorem

4. Transitive Property


4. ANS:

Converse: If a figure has four sides, then it is a rectangle.


5. ANS:

Converse: If a triangle is isosceles, then two angles in the triangle are congruent.


6. ANS:

Given: a is a transversal; ∠3 ≅ ∠6 or ∠4 ≅ ∠5

Prove: b Ä c


7. ANS:

Given: a Ä z, d is a transversal

Prove: ∠2 ≅ ∠7 or ∠6 ≅ ∠3


ID: A

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8. ANS:

Statements Reasons

1. ∠2 ≅ ∠7 and line k is a transversal

2. Angles 5 and 2 are vertical angles

3. ∠5 ≅ ∠2

4.∠5 ≅ ∠7

5. Angles 5 and 7 are corresponding angles

6. m Ä n

1. Given

2. Definition of vertical angles

3. Vertical Angles Congruence Theorem

4. Transitive Property

5. Definition of corresponding angles

6. Corresponding Angles Converse Postulate


9. ANS:

∠6 and ∠7 are supplementary- Given

∠5 and ∠6 are a linear pair- Definition of linear pair

∠5 and ∠6 are supplementary- Linear Pair Postulate

∠5 ≅ ∠7 - Corresponding Angle Postulate

g II f - Substitution Property


10. ANS:

octagon


11. ANS:

pentagon


12. ANS:

hexagon


13. ANS:

quadrilateral


14. ANS:

nonagon


ID: A

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15. ANS:

decagon


16. ANS:

hexagon


17. ANS:


18. ANS:


19. ANS:


20. ANS:

By the Corresponding Angle Postulate and the definition of congruent angles, m∠3 = m∠7. By the Linear

Pair Postulate and the definition of supplementary angles, m∠6 + m∠7 = 180°. Using the Substitution

Property, m∠6 + m∠3 = 180°. Then m∠6 = 180° − m∠3 = 180° − 26°. Thus, m∠6 = 154°.

PTS: 1 REF: Ch2.1 TOP: Mid Ch Test

ID: A

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21. ANS:

Students may use a flow chart or a two-column or paragraph proof. The flow chart proof is provided.

Students only need to use one method.

PTS: 1 REF: Ch2.3 TOP: End Ch Test

22. ANS:

m∠2 = 78° because ∠1 and ∠2 are supplementary angles.



m∠5 = 102° because ∠1and ∠5 are congruent corresponding angles.

m∠6 = 78° because ∠4 and ∠6 are congruent alternate interior angles.

m∠7 = 102° because ∠1and ∠7 are congruent alternate exterior angles.

m∠8 = 78° because ∠4 and ∠8 are congruent corresponding angles.

PTS: 1 REF: Ch2.6 TOP: End Ch Test

23. ANS:

a. a quadrilateral is a square

b. the quadrilateral is a rectangle

c. If a quadrilateral is a rectangle, then the quadrilateral is a square.

PTS: 1 REF: Ch2.1 TOP: Standard Test

ID: A

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24. ANS:

PTS: 1 REF: Ch2.2 TOP: Assignment

25. ANS:

7x − 14° = 5x + 18°

2x = 32°

x = 16°


26. ANS:

3x + 4x + 5° = 180°

7x = 175°

x = 25°


27. ANS:

a.11x + 4° + 5x = 180°

16x = 176°

m∠EGA = 11(11°) + 4 = 125°

x = 11°

b. m∠CHF = (5 ⋅ 11)° = 55°

c. m∠FHD = m∠EGA = 125°

d. m∠EGB = m∠CHF = 55°


ID: A

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28. ANS:

a. Alternate Exterior Angles Converse Theorem

b. Same-Side Interior Angles Converse Theorem

c. Corresponding Angles Postulate

d. Same-Side Exterior Angles Converse Theorem

e. Alternate Interior Angles Converse Theorem

f. Same-Side Interior Angles Theorem


29. ANS:

a. x Ä y; Alternate Interior Angles Converse Theorem

b. x Ä z; Same-Side Exterior Angles Converse Theorem

c. y Ä z; Corresponding Angles Converse Postulate

d. y Ä z; Same-Side Interior Angles Converse Theorem

e. x Ä y; Same-Side Exterior Angles Converse Theorem

f. x Ä z; Alternate Exterior Angles Converse Theorem


examview - ch 2 test review · ch 2 test review making conjectures: conjectures about angles formed...

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